ABC is a right angled triangle. D is the point on AB such that AD = 3DB. AC = 2DB and angle A = 90 degrees. Show that sinC = k/√20 where k is an integer. Find the value of k

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AB = 4DB

AC = 2DB

Find BC using Pythagoras:

BC = √(4DB)2 + (2DB)2

BC = √20DB2

= √20 DB

sinC = opp/hyp = 4DB/√20DB = 4/√20

so k = 4

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